More specifically, in tree-level Einstein-Yang Mills theory, soft gluon and graviton theorems were shown to supply enough structure to fix entirely the leading terms in gluon and graviton OPEs in a holomorphic limit [1]}. In this paper, we revisit the analysis of [1]} to determine OPE coefficients between massless particles of generic spin. We demonstrate that 4D translations together with 4D Lorentz (2D global conformal) symmetry alone completely determine the \(\Delta \) -dependence of OPE coefficients between celestial operators of arbitrary spin at leading order in a holomorphic limit at tree-level. The undetermined spin dependence of the OPE coefficients appears in the overall normalization and is effectively equivalent to the three-point coupling constant in a 4D effective action. We explicitly compare all symmetry-derived OPE coefficients against those derived from tree-level collinear limits of momentum-space scattering amplitudes and find precise agreement.
